975:
1863:
1884:
964:
1873:
180:, and not by the number of modes in particular resonance clusters – which can be fairly big. As a result, while SWT is completely described by statistical methods, in DWT both integrable and chaotic dynamics are accounted for. A graphical representation of a resonant cluster of wave components is given by the corresponding NR-diagram (
201:. Accordingly, three wave turbulent regimes can be singled out—kinetic, discrete and mesoscopic described by KZ-spectra, resonance clustering and their coexistence correspondingly. Energetic behavior of kinetic wave turbulent regime is usually described by
109:. That leads to an excitation of waves with frequencies and wavelengths in wide intervals, not necessarily in resonance with an external source. In experiments with high shaking amplitudes one initially observes waves that are in
164:
on the details of initial energy distribution over the wave field or on the initial magnitude of the complete energy in a wave turbulent system. Only the fact the energy is conserved at some inertial interval is important.
113:
with one another. Thereafter, both longer and shorter waves appear as a result of wave interaction. The appearance of shorter waves is referred to as a direct cascade while longer waves are part of an
105:
When, however, wave amplitudes are not very small (for surface waves: when the fluid surface is inclined by more than few degrees) waves with different frequencies start to
172:, are exact and quasi-resonances. Previous to the two-layer model of wave turbulence, the standard counterpart of SWT were low-dimensioned systems characterized by
140:, which allows using some statistical assumptions and describing the wave system by kinetic equations and their stationary solutions – the approach developed by
43:
106:
1603:
114:
1593:
652:
213:), while NR-diagrams are suitable for representing finite resonance clusters in discrete regime and energy cascades in mesoscopic regimes.
1509:
1876:
924:
692:
298:
1156:
645:
1046:
1751:
1178:
1066:
357:
1598:
869:
380:
334:
245:
86:
in some narrow interval. For example, shaking a container with frequency ω excites surface waves with frequency ω/2 (
1056:
1016:
1786:
772:
1866:
1459:
638:
914:
284:
974:
1909:
1111:
372:
290:
1646:
1051:
1011:
1776:
1151:
1141:
1081:
717:
687:
1813:
1796:
1633:
1126:
991:
929:
919:
812:
1808:
1746:
1173:
859:
187:
In some wave turbulent systems both discrete and statistical layers of turbulence are observed
1919:
1641:
1623:
1131:
1026:
661:
67:
495:; Korotkevich, A.O.; Pushkarev, A.N.; Dyachenko, A.I. (2005). "Mesoscopic wave turbulence".
1914:
1828:
1661:
1364:
1221:
1086:
797:
610:
561:
514:
492:
456:
409:
318:
229:
141:
87:
8:
1823:
1708:
1703:
1429:
1101:
1061:
777:
181:
35:
20:
622:
614:
565:
518:
460:
413:
160:
and α a positive constant depending on the specific wave system. The form of KZ-spectra
1766:
1479:
1469:
1434:
1334:
1319:
1216:
577:
551:
530:
504:
480:
446:
437:
Kartashova, E. (2007). "Exact and quasi-resonances in discrete water wave turbulence".
425:
399:
197:
1848:
1838:
1781:
1761:
1444:
1409:
1344:
1324:
1314:
1196:
884:
742:
534:
472:
376:
353:
330:
294:
241:
581:
484:
429:
1803:
1771:
1741:
1550:
1535:
1404:
1339:
1231:
1146:
1076:
1001:
782:
752:
682:
677:
618:
573:
569:
522:
464:
417:
63:
468:
1608:
1504:
1454:
1419:
1379:
1271:
1241:
1091:
1041:
951:
842:
767:
727:
349:
326:
237:
206:
91:
1718:
1713:
1618:
1613:
1449:
1389:
1384:
1116:
1006:
827:
762:
737:
598:
963:
421:
1903:
1888:
1736:
1656:
1545:
1464:
1439:
1374:
1304:
1211:
1106:
983:
904:
864:
837:
747:
697:
210:
99:
1843:
1791:
1731:
1682:
1560:
1555:
1530:
1514:
1489:
1206:
1096:
1036:
822:
732:
707:
476:
120:
51:
102:– only those waves exist that are directly excited by an external source.
1833:
1565:
1494:
1359:
1299:
1266:
1256:
1251:
1136:
1071:
1031:
1021:
996:
879:
852:
832:
792:
757:
39:
630:
509:
451:
404:
1651:
1499:
1474:
1369:
1349:
1276:
1261:
1246:
1236:
1201:
1121:
941:
936:
899:
894:
889:
787:
157:
145:
83:
1883:
526:
78:
External sources by some resonant mechanism usually excite waves with
1723:
1585:
1570:
1484:
1329:
1168:
1163:
946:
874:
802:
722:
712:
669:
491:
192:
110:
95:
79:
28:
1818:
1540:
1399:
1291:
1281:
1226:
702:
556:
1687:
1677:
847:
817:
202:
1394:
807:
47:
125:
Two generic types of wave turbulence should be distinguished:
1756:
1575:
1354:
1309:
16:
Set of nonlinear waves deviated far from thermal equilibrium
1188:
59:
55:
31:
390:
Kartashova, E. (2006). "A model of laminated turbulence".
98:
are small – which usually means that the wave is far from
121:
Statistical wave turbulence and discrete wave turbulence
317:
228:
323:
Kolmogorov
Spectra of Turbulence I – Wave Turbulence
234:
Kolmogorov
Spectra of Turbulence I – Wave Turbulence
191:, this wave turbulent regime have been described in
542:Kartashova, E. (2009). "Discrete wave turbulence".
1604:North West Shelf Operational Oceanographic System
1901:
148:–Zakharov (KZ) energy spectra and have the form
1594:Deep-ocean Assessment and Reporting of Tsunamis
646:
276:
597:
653:
639:
541:
436:
389:
282:
271:
260:
169:
660:
555:
508:
450:
403:
38:. Such a state is usually accompanied by
168:The subject of DWT, first introduced in
601:; Rumpf, B. (2011). "Wave turbulence".
50:to sustain it. Examples are waves on a
1902:
925:one-dimensional Saint-Venant equations
321:; Lvov, V.S.; Falkovich, G.E. (1992).
232:; Lvov, V.S.; Falkovich, G.E. (1992).
138:exact and quasi-resonances are omitted
634:
1872:
623:10.1146/annurev-fluid-122109-160807
176:. However, DWT is characterized by
13:
1752:National Oceanographic Data Center
1179:World Ocean Circulation Experiment
1067:Global Ocean Data Analysis Project
590:
46:or requires an external source of
14:
1931:
1599:Global Sea Level Observing System
1882:
1871:
1862:
1861:
1057:Geochemical Ocean Sections Study
973:
962:
603:Annual Review of Fluid Mechanics
174:a small number of modes included
1787:Ocean thermal energy conversion
1510:Vine–Matthews–Morley hypothesis
343:
265:
254:
222:
1:
469:10.1103/PhysRevLett.98.214502
310:
144:. These solutions are called
73:
1047:El Niño–Southern Oscillation
1017:Craik–Leibovich vortex force
773:Luke's variational principle
366:
286:Nonlinear Resonance Analysis
7:
367:Galtier, Sebastien (2023).
127:statistical wave turbulence
10:
1936:
1112:Ocean dynamical thermostat
960:
574:10.1209/0295-5075/87/44001
373:Cambridge University Press
369:Physics of Wave Turbulence
344:Nazarenko, Sergey (2011).
291:Cambridge University Press
1857:
1696:
1670:
1647:Ocean acoustic tomography
1632:
1584:
1523:
1460:Mohorovičić discontinuity
1418:
1290:
1187:
1052:General circulation model
982:
688:Benjamin–Feir instability
668:
422:10.1134/S0021364006070058
1777:Ocean surface topography
1152:Thermohaline circulation
1142:Subsurface ocean current
1082:Hydrothermal circulation
915:Wave–current interaction
693:Boussinesq approximation
216:
131:discrete wave turbulence
1814:Sea surface temperature
1797:Outline of oceanography
992:Atmospheric circulation
930:shallow water equations
920:Waves and shallow water
813:Significant wave height
439:Physical Review Letters
283:Kartashova, E. (2010).
1809:Sea surface microlayer
1174:Wind generated current
445:(21): 214502 (4 pp.).
193:Zakharov et al. (2005)
1642:Deep scattering layer
1624:World Geodetic System
1132:Princeton Ocean Model
1012:Coriolis–Stokes force
662:Physical oceanography
68:electromagnetic waves
1662:Underwater acoustics
1222:Perigean spring tide
1087:Langmuir circulation
798:Rossby-gravity waves
550:(4): 44001 (5 pp.).
178:resonance clustering
142:Vladimir E. Zakharov
117:of wave turbulence.
88:parametric resonance
1824:Science On a Sphere
1430:Convergent boundary
1102:Modular Ocean Model
1062:Geostrophic current
778:Mild-slope equation
615:2011AnRFM..43...59N
566:2009EL.....8744001K
519:2005physics...8155Z
461:2007PhRvL..98u4502K
414:2006JETPL..83..283K
182:nonlinear resonance
44:decaying turbulence
36:thermal equilibrium
21:continuum mechanics
1480:Seafloor spreading
1470:Outer trench swell
1435:Divergent boundary
1335:Continental margin
1320:Carbonate platform
1217:Lunitidal interval
34:deviated far from
1910:Nonlinear systems
1897:
1896:
1889:Oceans portal
1849:World Ocean Atlas
1839:Underwater glider
1782:Ocean temperature
1445:Hydrothermal vent
1410:Submarine volcano
1345:Continental shelf
1325:Coastal geography
1315:Bathymetric chart
1197:Amphidromic point
885:Wave nonlinearity
743:Infragravity wave
527:10.1134/1.2150867
300:978-0-521-76360-8
272:Kartashova (2009)
261:Kartashova (2007)
170:Kartashova (2006)
1927:
1887:
1886:
1875:
1874:
1865:
1864:
1804:Pelagic sediment
1742:Marine pollution
1536:Deep ocean water
1405:Submarine canyon
1340:Continental rise
1232:Rule of twelfths
1147:Sverdrup balance
1077:Humboldt Current
1002:Boundary current
977:
966:
783:Radiation stress
753:Iribarren number
728:Equatorial waves
683:Ballantine scale
678:Airy wave theory
655:
648:
641:
632:
631:
626:
585:
559:
538:
512:
488:
454:
433:
407:
386:
363:
340:
305:
304:
280:
274:
269:
263:
258:
252:
251:
226:
90:, discovered by
1935:
1934:
1930:
1929:
1928:
1926:
1925:
1924:
1900:
1899:
1898:
1893:
1881:
1853:
1692:
1666:
1628:
1609:Sea-level curve
1580:
1519:
1505:Transform fault
1455:Mid-ocean ridge
1421:
1414:
1380:Oceanic plateau
1286:
1272:Tidal resonance
1242:Theory of tides
1183:
1092:Longshore drift
1042:Ekman transport
978:
972:
971:
970:
969:
968:
967:
958:
910:Wave turbulence
843:Trochoidal wave
768:Longshore drift
664:
659:
629:
593:
591:Further reading
588:
510:physics/0508155
452:math-ph/0701077
405:physics/0512014
383:
360:
350:Springer-Verlag
346:Wave Turbulence
337:
327:Springer-Verlag
313:
308:
301:
281:
277:
270:
266:
259:
255:
248:
238:Springer-Verlag
227:
223:
219:
211:Wyld's diagrams
162:does not depend
123:
115:inverse cascade
92:Michael Faraday
76:
62:, and waves in
42:. It is either
25:wave turbulence
17:
12:
11:
5:
1933:
1923:
1922:
1917:
1912:
1895:
1894:
1892:
1891:
1879:
1869:
1858:
1855:
1854:
1852:
1851:
1846:
1841:
1836:
1831:
1829:Stratification
1826:
1821:
1816:
1811:
1806:
1801:
1800:
1799:
1789:
1784:
1779:
1774:
1769:
1764:
1759:
1754:
1749:
1744:
1739:
1734:
1729:
1721:
1719:Color of water
1716:
1714:Benthic lander
1711:
1706:
1700:
1698:
1694:
1693:
1691:
1690:
1685:
1680:
1674:
1672:
1668:
1667:
1665:
1664:
1659:
1654:
1649:
1644:
1638:
1636:
1630:
1629:
1627:
1626:
1621:
1619:Sea level rise
1616:
1614:Sea level drop
1611:
1606:
1601:
1596:
1590:
1588:
1582:
1581:
1579:
1578:
1573:
1568:
1563:
1558:
1553:
1548:
1543:
1538:
1533:
1527:
1525:
1521:
1520:
1518:
1517:
1512:
1507:
1502:
1497:
1492:
1487:
1482:
1477:
1472:
1467:
1462:
1457:
1452:
1450:Marine geology
1447:
1442:
1437:
1432:
1426:
1424:
1416:
1415:
1413:
1412:
1407:
1402:
1397:
1392:
1390:Passive margin
1387:
1385:Oceanic trench
1382:
1377:
1372:
1367:
1362:
1357:
1352:
1347:
1342:
1337:
1332:
1327:
1322:
1317:
1312:
1307:
1302:
1296:
1294:
1288:
1287:
1285:
1284:
1279:
1274:
1269:
1264:
1259:
1254:
1249:
1244:
1239:
1234:
1229:
1224:
1219:
1214:
1209:
1204:
1199:
1193:
1191:
1185:
1184:
1182:
1181:
1176:
1171:
1166:
1161:
1160:
1159:
1149:
1144:
1139:
1134:
1129:
1124:
1119:
1117:Ocean dynamics
1114:
1109:
1104:
1099:
1094:
1089:
1084:
1079:
1074:
1069:
1064:
1059:
1054:
1049:
1044:
1039:
1034:
1029:
1024:
1019:
1014:
1009:
1007:Coriolis force
1004:
999:
994:
988:
986:
980:
979:
961:
959:
957:
956:
955:
954:
944:
939:
934:
933:
932:
927:
917:
912:
907:
902:
897:
892:
887:
882:
877:
872:
867:
862:
857:
856:
855:
845:
840:
835:
830:
828:Stokes problem
825:
820:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
763:Kinematic wave
760:
755:
750:
745:
740:
735:
730:
725:
720:
715:
710:
705:
700:
695:
690:
685:
680:
674:
672:
666:
665:
658:
657:
650:
643:
635:
628:
627:
594:
592:
589:
587:
586:
539:
503:(8): 487–491.
493:Zakharov, V.E.
489:
434:
398:(7): 283–287.
387:
381:
364:
359:978-3642159411
358:
341:
335:
319:Zakharov, V.E.
314:
312:
309:
307:
306:
299:
275:
264:
253:
246:
230:Zakharov, V.E.
220:
218:
215:
195:and is called
189:simultaneously
136:In SWT theory
122:
119:
94:). When wave
75:
72:
15:
9:
6:
4:
3:
2:
1932:
1921:
1918:
1916:
1913:
1911:
1908:
1907:
1905:
1890:
1885:
1880:
1878:
1870:
1868:
1860:
1859:
1856:
1850:
1847:
1845:
1842:
1840:
1837:
1835:
1832:
1830:
1827:
1825:
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1805:
1802:
1798:
1795:
1794:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1765:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1737:Marine energy
1735:
1733:
1730:
1728:
1727:
1722:
1720:
1717:
1715:
1712:
1710:
1707:
1705:
1704:Acidification
1702:
1701:
1699:
1695:
1689:
1686:
1684:
1681:
1679:
1676:
1675:
1673:
1669:
1663:
1660:
1658:
1657:SOFAR channel
1655:
1653:
1650:
1648:
1645:
1643:
1640:
1639:
1637:
1635:
1631:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1591:
1589:
1587:
1583:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1557:
1554:
1552:
1549:
1547:
1544:
1542:
1539:
1537:
1534:
1532:
1529:
1528:
1526:
1522:
1516:
1513:
1511:
1508:
1506:
1503:
1501:
1498:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1478:
1476:
1473:
1471:
1468:
1466:
1465:Oceanic crust
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1440:Fracture zone
1438:
1436:
1433:
1431:
1428:
1427:
1425:
1423:
1417:
1411:
1408:
1406:
1403:
1401:
1398:
1396:
1393:
1391:
1388:
1386:
1383:
1381:
1378:
1376:
1375:Oceanic basin
1373:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1351:
1348:
1346:
1343:
1341:
1338:
1336:
1333:
1331:
1328:
1326:
1323:
1321:
1318:
1316:
1313:
1311:
1308:
1306:
1305:Abyssal plain
1303:
1301:
1298:
1297:
1295:
1293:
1289:
1283:
1280:
1278:
1275:
1273:
1270:
1268:
1265:
1263:
1260:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1225:
1223:
1220:
1218:
1215:
1213:
1212:Internal tide
1210:
1208:
1205:
1203:
1200:
1198:
1195:
1194:
1192:
1190:
1186:
1180:
1177:
1175:
1172:
1170:
1167:
1165:
1162:
1158:
1155:
1154:
1153:
1150:
1148:
1145:
1143:
1140:
1138:
1135:
1133:
1130:
1128:
1125:
1123:
1120:
1118:
1115:
1113:
1110:
1108:
1107:Ocean current
1105:
1103:
1100:
1098:
1095:
1093:
1090:
1088:
1085:
1083:
1080:
1078:
1075:
1073:
1070:
1068:
1065:
1063:
1060:
1058:
1055:
1053:
1050:
1048:
1045:
1043:
1040:
1038:
1035:
1033:
1030:
1028:
1025:
1023:
1020:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
989:
987:
985:
981:
976:
965:
953:
950:
949:
948:
945:
943:
940:
938:
935:
931:
928:
926:
923:
922:
921:
918:
916:
913:
911:
908:
906:
905:Wave shoaling
903:
901:
898:
896:
893:
891:
888:
886:
883:
881:
878:
876:
873:
871:
868:
866:
865:Ursell number
863:
861:
858:
854:
851:
850:
849:
846:
844:
841:
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749:
748:Internal wave
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729:
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698:Breaking wave
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52:fluid surface
49:
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37:
33:
30:
26:
22:
1920:Oceanography
1844:Water column
1792:Oceanography
1767:Observations
1762:Explorations
1732:Marginal sea
1725:
1683:OSTM/Jason-2
1515:Volcanic arc
1490:Slab suction
1207:Head of tide
1097:Loop Current
1037:Ekman spiral
909:
823:Stokes drift
733:Gravity wave
708:Cnoidal wave
609:(1): 59–78.
606:
602:
599:Newell, A.C.
547:
543:
500:
497:JETP Letters
496:
442:
438:
395:
392:JETP Letters
391:
368:
345:
322:
285:
278:
267:
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233:
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126:
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104:
77:
27:is a set of
24:
18:
1915:Water waves
1834:Thermocline
1551:Mesopelagic
1524:Ocean zones
1495:Slab window
1360:Hydrography
1300:Abyssal fan
1267:Tidal range
1257:Tidal power
1252:Tidal force
1137:Rip current
1072:Gulf Stream
1032:Ekman layer
1022:Downwelling
997:Baroclinity
984:Circulation
880:Wave height
870:Wave action
853:megatsunami
833:Stokes wave
793:Rossby wave
758:Kelvin wave
738:Green's law
84:wavelengths
80:frequencies
66:excited by
54:excited by
40:dissipation
1904:Categories
1772:Reanalysis
1671:Satellites
1652:Sofar bomb
1500:Subduction
1475:Ridge push
1370:Ocean bank
1350:Contourite
1277:Tide gauge
1262:Tidal race
1247:Tidal bore
1237:Slack tide
1202:Earth tide
1122:Ocean gyre
942:Wind setup
937:Wind fetch
900:Wave setup
895:Wave radar
890:Wave power
788:Rogue wave
718:Dispersion
325:. Berlin:
311:References
236:. Berlin:
198:mesoscopic
184:diagram).
158:wavenumber
146:Kolmogorov
129:(SWT) and
96:amplitudes
74:Appearance
1634:Acoustics
1586:Sea level
1485:Slab pull
1422:tectonics
1330:Cold seep
1292:Landforms
1169:Whirlpool
1164:Upwelling
947:Wind wave
875:Wave base
803:Sea state
723:Edge wave
713:Cross sea
557:0907.4406
535:119002924
111:resonance
29:nonlinear
1867:Category
1819:Seawater
1546:Littoral
1541:Deep sea
1400:Seamount
1282:Tideline
1227:Rip tide
1157:shutdown
1127:Overflow
860:Undertow
703:Clapotis
582:18241042
485:12248807
477:17677779
430:15630550
207:diagrams
107:interact
100:breaking
1877:Commons
1747:Mooring
1697:Related
1688:Jason-3
1678:Jason-1
1561:Pelagic
1556:Oceanic
1531:Benthic
848:Tsunami
818:Soliton
611:Bibcode
562:Bibcode
515:Bibcode
457:Bibcode
410:Bibcode
203:Feynman
152:, with
133:(DWT).
1566:Photic
1395:Seabed
808:Seiche
580:
533:
483:
475:
428:
379:
356:
333:
297:
244:
209:(i.e.
205:-type
64:plasma
48:energy
1757:Ocean
1726:Alvin
1576:Swash
1420:Plate
1365:Knoll
1355:Guyot
1310:Atoll
1189:Tides
952:model
838:Swell
670:Waves
578:S2CID
552:arXiv
531:S2CID
505:arXiv
481:S2CID
447:arXiv
426:S2CID
400:arXiv
217:Notes
70:etc.
60:ships
56:winds
32:waves
1724:DSV
1709:Argo
1571:Surf
1027:Eddy
473:PMID
377:ISBN
354:ISBN
331:ISBN
295:ISBN
242:ISBN
156:the
82:and
619:doi
570:doi
544:EPL
523:doi
465:doi
418:doi
58:or
19:In
1906::
617:.
607:43
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150:k
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